In this study, robust Brown-Forsythe and robust Modified Brown-Forsythe ANOVA tests are proposed to take into consideration heteroscedastic and non-normality data sets with outliers. The non-normal data is assumed to be a two parameters Weibull distribution. Robust proposed tests are obtained by using robust mean and variance estimators based on median/MAD and median/Qn methods instead of maximum likelihood. The behaviors of the robust proposed and classical ANOVA tests are examined by simulation study. The results shows that the proposed robust tests have good performance especially in the presence of heteroscedasticity and contamination.